As the presidential contenders prepared for their second debate in Nashville last night, 8,000 miles away in the heart of Africa Barack Obama’s grandmother was rooting for the man she calls “Barry”.

Sarah Onyango Obama is not the first person to look on anxiously as a relative aspires to the most powerful office in the world, but she is surely the first to do so from a two-roomed, tin-roofed African hut with chickens picking around her bare feet.

Watching her grandson campaigning in the run-up to last night’s debate, the 87-year-old matriarch of the Obama clan nodded with excitement at every phrase, though she speaks no English.

Her flickering television is powered by a newly installed solar panel, for there is no mains electricity here. Outside, multicoloured butterflies flit around the mango and avocado trees and the midday heat is leaden.

We are in the ancestral homeland of the Obamas, near the shores of Lake Victoria a few miles north of the equator, 300 miles (480km) northwest of Nairobi, and as far as it is possible to imagine from the White House.

Kogelo, a patch of rust-red earth near Kenya’s border with Uganda, is where Mr Obama’s father was born and buried and where his forebears in the Luo tribe raised goats and cattle for centuries; it is the place where, by his own account, the Democratic candidate discovered his identity, as the child of an American mother and Kenyan father.

As Mr Obama’s stump speech came to an end, the woman he calls “Granny Sarah” and her African neighbours joined in a chorus of ululation, the wavering, high-pitched call of African celebration, and the startled chickens skittered away.

On Mr Obama’s long, strange journey towards the presidency, Kogelo is the starting point. “I think he is going to win,” said Granny Sarah in Luo, while her son, Sayid Obama – Barack’s uncle – translated. Then she flashed a huge grin. “I shall certainly go to the inauguration.”

If Mr Obama wins, the Kenyan delegation will be a large one, for his African family tree isfabulously complicated. Strictly speaking, Sarah Onyango is Obama’s step-grandmother, who raised his father, Barack Obama Senior, after his own mother left. Barack Obama Sr had at least eight children, by at least four women.

The Democratic candidate barely knew his Kenyan father, who died in a car crash in 1982. Intelligent, charming and feckless, Barack Obama Sr arrived at the University of Hawaii in 1959, married an 18-year-old white woman, Ann Dunham, sired Barack Obama and then left.

For some American voters the extraordinary story of how Barack Obama discovered his African roots is part of his appeal, but for others his childhood in Hawaii and Indonesia, and his African heritage, are simply too exotic. Mr Obama’s opponents have seized on his sprawling African family as a political weapon.

Yet Mr Obama is plainly proud of his Kenyan bloodline. Around the walls of her hut, Sarah Obama displays numerous photos of the candidate and his family, and a poster for his first Senatorial campaign on which Mr Obama has written. “Habariuku Mama Sarah”, Swahili for “Hello Granny Sarah”.

She pointed to a faded framed photograph of a young Mr Obama, beaming alongside his grandmother, and carrying a large sack: “I was very happy when he came here. He carried my vegetables to the market.”

Mr Obama described his first visit to Kenya in an autobiography, Dreams from My Father. At 27, Mr Obama was a confused young man searching for an identity and troubled by his mixed racial heritage, turning to drink and drugs to “push questions of who I was out of my mind”.

The young Mr Obama travelled to Kogelo by matatu, the cramped, garishly decorated species of minibus that means “room for three more” in Swahili. He was greeted at the family compound by his step-grandmother with the words: “Finally you have come home.”

Mr Obama’s grandfather Hussein Onyango Obama, Sarah’s husband, was a herbalist and village elder, but he was also a progressive, the first man in the village to swap goatskins for trousers. He fought in British uniform during the Second World War, returning with a gramophone and a picture of a white woman he claimed to have married in Burma.

The picture, a framed etching of a female aristocrat with long black hair, hangs alongside the photos of Mr Obama. “She is very beautiful,” said Sarah Onyango.

Mr Onyango retained a respect for British ways and education, even after the British locked him up on suspicion of anticolonial agitation. “King George and Queen Elizabeth gave us schools,” says Granny Sarah.

Mr Onyango, who died in 1975 at the age of 105, toyed with Christianity, and briefly changed his name to Johnson – would Barack Hussein Obama be more, or less electable as “Barry Johnson”? He rejected Christianity later as “foolish sentiment” and converted to Islam. Although the family still takes Arabic names (Barack means blessed), their faith is so lightly worn as to be invisible.

During that first visit, Mr Obama discovered the truth about his father. Far from being the postcolonial hero his son had imagined, Barack Obama Sr never lived up to his early promise, ending life as “a bitter drunk”, a “defeated bureaucrat” and an “abusive husband” with a string of unhappy relationships and multiple children he could not support.

In his book Mr Obama described the catharsis he experienced at his father’s graveside in Kogelo: “I felt the circle finally close. I saw that my life in America – the black life, the white life, the sense of abandonment I’d felt as a boy . . . all of it was connected with this small plot of land an ocean away.”

Mr Obama’s visit to Kogelo changed him forever. It also changed Kogelo. The school has been renamed “Senator Obama Secondary School”, babies named Obama are now common and even Raila Odinga, the Kenyan Prime Minister, has claimed kinship with the candidate.

On the way to Kogelo we spotted a matatu, similar to the vehicle that brought him here in 1988, decorated with a huge dollar bill and the candidate’s face, “Obama – King of our Hearts”. Many Kenyans see Mr Obama’s election as an opportunity for the country, and are likely to be disappointed. “People think there will be a direct benefit but he’s American, he’s not our president” said Sayid.

In another sign that the election has changed life in Kogelo, an eight-foot fence is being erected around the compound to keep out unwanted visitors.

At the Democratic convention in 2004 Mr Obama declared: “Let’s face it, my presence on this stage is pretty unlikely. My father was born and raised in a village in Kenya. He grew up herding goats, went to school in a shack. His father, my grandfather, was a cook, a domestic servant.”

Mr Obama’s African roots have been used by some opponents to hint that he is not quite American, or is a closet Muslim. Right-wing talk show hosts emphasise his middle name, Hussein. A lawsuit has been filed claiming that he was born in Kenya, and is therefore ineligible for the presidency. Italian Vanity Fair revealed recently that Mr Obama’s half-brother, George Hussein Obama, the youngest child of Barack Obama Sr, was living in one of Nairobi’s largest slums. A Republican attack advertisement showed a picture of Barack Obama’s large home in Chicago juxtaposed with George’s humble shack: “If Obama cares so much for your family, why doesn’t he take care of his own family first?” In his memoir, Mr Obama recalled George as a six-year-old “with a wary gaze”. “If he ever came to me, I would be there for him,” he wrote.

George Obama’s gaze was understandably wary when he met me at a Nairobi restaurant. Now 26, he knows that he has become a factor in the US presidential election. “They are comparing the way I live to the way he lives,” he said. “They compare my world with his world. I have a good life. It’s not like I live in the gutter. I’m happy with the way I live.”

From the shade of the baobab tree at Kogelo compound, it is staggering to reflect on the cultural leap made by the Obama family in a generation – and its profound effects on all of them.

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